Highly efficient XUV generation via high-order frequency mixing

The efficient generation of the coherent XUV light via frequency conversion of intense laser drivers is a problem of both fundamental and technological importance. Increasing the intensity of the generated high harmonics by raising the intensity of the driving field works only up to a point: at high intensities, rapid ionisation of the medium limits the conversion efficiency. Considering the combined effect of the phase-matching and of the blue shift of the driving field during its propagation in a rapidly ionising medium, we show that the latter can be the dominant limiting mechanism. We introduce a new spatial scale, the blue-shift length, which sets the upper bound for the quadratic intensity growth of the generated harmonics. Moreover, we show that this seemingly fundamental restriction can be overcome by using an additional generating weak mid-IR field. For specific combinations of frequencies of the generating fields, the corresponding high-order frequency-mixing process does not suffer from the blue shift of the drivers and phase mismatch, and thus its efficiency grows quadratically with propagation distance. Our results thus open a new route for highly efficient generation of coherent XUV light.